Question

What is the measure of $\angle x$, if m(arc CD) is ${100}^o$ and m (arc BE) is ${40}^o$?

• A. ${60}^o$
• B. ${40}^o$
• C. ${30}^o$
• D. ${10}^o$

Answer 1

The correct option is C ${30}^o$

Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs
$\angle x=\frac{(arcofCD-arcofBE)}{2}$
$\angle x=\frac{({100}^o-{40}^o)}{2}$
$\angle x=\frac{{60}^o}{2}={30}^o$